How to add custom function to pre-existing buttons in Blender 2.8?
Why reinvent the wheel?

If you press play the pause button is shown and vice versa.  Turn on developer extras and view source and will find 

if not screen.is_animation_playing:


to draw the pause button. screen is the context screen.

Hence your boolean property could be replaced by or driven with bpy.types.Screen.is_animation_playing

Notice it belongs to screen not scene as it can be set on a per screen basis.